Electron. J. Diff. Equ., Vol. 2012 (2012), No. 231, pp. 1-12.

Solutions to a partial integro-differential parabolic system arising in the pricing of financial options in regime-switching jump diffusion models

Ionut Florescu, Ruihua Liu, Maria Cristina Mariani

We study a complex system of partial integro-differential equations (PIDE) of parabolic type modeling the option pricing problem in a regime-switching jump diffusion model. Under suitable conditions, we prove the existence of solutions of the PIDE system in a general domain by using the method of upper and lower solutions.

Submitted December 15, 2011. Published December 21, 2012.
Math Subject Classifications: 35K99, 35F99, 45K05, 45K99.
Key Words: Partial integro-differential equations; option pricing; regime-switching jump diffusion; upper and lower solutions.

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Ionut Florescu
Department of Mathematical Sciences
Stevens Institute of Technology
Castle Point on Hudson, Hoboken, NJ 07030, USA
email: Ionut.Florescu@stevens.edu
Ruihua Liu
Department of Mathematics
University of Dayton
300 College Park, Dayton, OH 45469-2316, USA
email: rliu01@udayton.edu
Maria Cristina Mariani
Department of Mathematical Sciences
The University of Texas at El Paso
Bell Hall 124, El Paso, TX 79968-0514, USA
email: mcmariani@utep.edu

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